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Boling Guo
Public Documents
6
Well-posedness, wave breaking, Holder continuity and periodic peakons for a nonlocal...
Guoquan Qin
and 2 more
December 30, 2021
In this paper, we investigate the initial value problem of a nonlocal sine-type µ-Camassa-Holm (µCH) equation, which is the µ-version of the sine-type CH equation. We first discuss its local well-posedness in the framework of Besov spaces. Then a sufficient condition on the initial data is provided to ensure the occurance of the wave-breaking phenomenon. We finally prove the H¨older continuity of the data-to-solution map, and find the explicit formula of the global weak periodic peakon solution.
A Nonhomogeneous Boundary-Valued Problem for the coupled KDV system
Yitong Pei
and 1 more
March 13, 2021
In this paper, we study the initial-boundary-value problem (IBVP) for coupled Korteweg-de Vries equations posed on a finite interval with nonhomogeneous boundary conditions. We overcome the requirement for stronger smooth boundary conditions in the traditional method via the Laplace transform. Our approach uses the strong Kato smoothing property and the contraction mapping principle.
Well posedness for the Kawahara equation on the half-line
Boling Guo
and 1 more
December 13, 2020
We study the low-regularity properties of the Kawahara equation on the half line. We obtain the local existence, uniqueness, and continuity of the solution. Moreover, We obtain that the nonlinear terms of the solution are smoother than the initial data.
The exponential behavior of 3D stochastic primitive equations driven by fractional no...
Lidan Wang
and 2 more
May 23, 2020
In this article, we study the exponential behavior of 3D stochastic primitive equations driven by fractional noise. Since fractional Brownian motion is essentially different from Brownian motion, the standard method via classic stochastic analysis tools is not available. Here, we develop a method which is close to the method from dynamic system to show that the weak solutions to 3D stochastic primitive equations driven by fractional noise converge exponentially to the unique stationary solution of primitive equations. This method may be applied to other stochastic hydrodynamic equations and other noises including Brownian motion and Lévy noise.
Global attractors of the periodic initial value problem for Landau--Lifshitz--Bloch--...
Boling Guo
and 2 more
August 08, 2020
This paper is devoted to study the global attractors of the periodic initial value problem for Landau--Lifshitz--Bloch--Maxwell system. Fist we give the global existence of the smooth solution for this system. Then, we prove the existence of global attractors, the Hausdorff dimension and fractal dimension have been estimated.
The fractal dimension of pullback attractors for the 2D Navier-Stokes equations with...
Xinguang Yang
and 3 more
April 27, 2020
This paper is concerned with the bounded fractal and Hausdorff dimension of the pullback attractors for 2D non-autonomous incompressible Navier-Stokes equations with constant delay terms. Using the construction of trace formula with two bases for phase spaces of product flow, the upper boundedness of fractal dimension has been achieved.